Find the greatest common factor of $36$ and $60$.
Answer: The greatest common factor (GCF) is the largest number that is a factor of both $36$ and $60$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}36 &=2\cdot2\cdot3\cdot3\\\\\\\\ 60&=2\cdot2\cdot3\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}36 &=2\cdot2\cdot3\cdot3\\\\\\\\ 60&=2\cdot2\cdot3\cdot5 \end{aligned}$ Each number shares the factors ${2}, {2},$ and $3,$ so the GCF is $2\cdot2\cdot3={12}$. The greatest common factor of $36$ and $60$ is $12$.